Please note that initially, all topics and readings are based an earlier version of this course. They are likely to change (or at least, change weeks) as the course progresses. At any rate, I will update this page very often. Bookmark it, and check it frequently to see what's going on in class.
|
Dates |
Topics |
Reading |
Homework |
Miscellaney |
|---|---|---|---|---|
| 1/13-1/15 |
Subharmonic functions |
G&K 7.6; see also 11.1,3,4 in Nar |
homework 1 |
Starting
Friday 1/15, we'll meet in Hayes Healy 117 instead of 127.
We're switching with another math class that was bursting at the seams
in 117. |
| 1/18-1/22 |
Perron's solution of the Dirichlet problem |
G&K 7.8; see also Nar 11.7 |
||
| 1/25-1/29 |
think about topics for your project |
I'll be away at a meeting this week, so there'll be no classes. In order make up the lost lectures, we'll start 5 minutes earlier and end 5 minutes later from 2/1 (the day I get back) til 3/5 (the day before spring break) | ||
| 2/1-2/5 |
analytic continuation, monodromy theorem. |
G&K chapter 10, see also Nar 2.2 and 2.4 |
homework 2 |
While
I'll be following Greene and Krantz here, the right language for
analytic continuation (and many, many other things) is that of
`sheaves'; Narasihman discusses sheaves in his book. Forster
discusses them more (and better). |
| 2/8-2/12 |
elliptic modular function and applications | G&K 10.5 |
||
| 2/15-2/19 |
elliptic modular function (cont) |
homework 3 |
My approach differs substantially from that of
G&K, using Schwarz reflection more and the modular group less. |
|
| 2/22-2/26 |
introduction to complex dynamics | In Gamelin's book (reserve) sections XII.3-5
treat this topic, albeit only for polynomials. |
There are several good book length introduction's
to complex dynamics. Beardon's "Iteration of Rational Functions"
is a fairly elementary treatment. Our library has it, but you'll
need to recall it--someone seems to have it checked out. |
|
| 3/1-3/5 |
More complex dynamics |
|||
| 3/15-3/19 |
Riemann surfaces | Gamelin 16.1-3, also see Forster 1.1-2 |
homework 4 |
|
| 3/22-3/26 | Uniformization |
|||
| 3/29-4/2 |
(cont) |
|||
| 4/5-4/9 |
(cont) |
|||
| 4/12-4/16 |
Sheaf cohomology & existence of meromorphic
functions |
Narasimhan, chapter 9. Especially sections 3, 5 and 6 |
Homework 4 is now updated. Santosh speaks MW 4/12 & 4/14. |
|
| 4/19-4/23 |
Presentations |
Tim speaks Wed 4/21 Han speaks Friday 4/23 |
||
| 4/26-4/28 |
Presentations |
Brian speaks Mon 4/26 Douglas speaks Wed 4/28 Please turn in the paper for your presentation and your final hwk by Wed, May 5 |